超越亚纯函数的拟亏值

Acta mathematica scientia,Series A ›› 2014, Vol. 34 ›› Issue (6): 1474-1480.

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Valiron Quasi-Deficient of Meromorphic Functions

LIU Dan¹, DENG Bing-Mao², YANG De-Gui¹

1.Department of Mathematics, College of Science, South China Agricultural University, Guangzhou 510642;
2.South China Institute of Software Engineering, Guangzhou University, Guangzhou 510990

Received:2013-03-05 Revised:2014-05-27 Online:2014-12-25 Published:2014-12-25
Supported by:
国家自然科学基金 (11371149, 61375006) 资助

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Abstract

Abstract:

Let f(z) be a transcendental meromorphic function, and let 0<δ< 1, if

lim—_r→∞log T(r+1/r,f )/log T(r, f)<+∞,

then there exist a_n (n=1, 2, …), such that the set {a: ?₁₎(a, f)>δ} is a subset of

∩^∞_j=1∪^∞_n=j{a:|a-a_n|<e-^enσ},

which means {a:Δ₁₎(a, f)>δ} is a set of finite μ-measure.

Key words: Meromorphic functions, Valiron quasi-deficient, μ-Measure

CLC Number:

30D35

Cite this article

LIU Dan, DENG Bing-Mao, YANG De-Gui. Valiron Quasi-Deficient of Meromorphic Functions[J].Acta mathematica scientia,Series A, 2014, 34(6): 1474-1480.

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[3] Furruta M, Toda N. On exceptional value of meromorphic functions of divergence class.J Japan Math Soc, 1973, 25(4): 667--679

[4] 方明亮, 郭辉. 亚纯函数的修正Valiron拟亏值. 四川师范学院学报(自然科学版), 1992, 13(2): 111--117

[5] 杨乐. 值分布论及其新研究. 北京: 科学出版社, 1995

[6] Gol'dberg A, Ostrovskii I. Value Distribution of Meromorphic Functions. Translations of Mathematical Monographs, 236,
Providence, RI: American Mathematical Society, 2008

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